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X₁₅₆₀¶

ORTHOJOIN OF X₄₆₈

X₁₅₆₀ (ORTHOJOIN OF X₄₆₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1560 = ORTHOJOIN OF X_468."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01560(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1560 = ORTHOJOIN OF X_468 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_67 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_67", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center"])
            central_line(model, X_6, X_67, 6, 67)
            central_line(model, X_2, X_112, 2, 112)
            X_1560 = intersect_lines(model, X_6, X_67, X_2, X_112, ID="X_1560", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            central_line(model, X_4, X_111, 4, 111, incident=True)
            return promote_point_to_top(model, X_1560)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_1560 on the given reference triangle."""
            model = create_model('X_1560 = ORTHOJOIN OF X_468')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01560(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-01560.json"))
            write_center_svg(
                model_acute,
                here / "x-01560.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1560¶

X₁₅₆₀¶